it's not clear exactly what you mean by "separated." If you have been living apart but are still legally married, do what Bsch4477 said above.
On the other hand, if you are "legally separated under a divorce or separate maintenance decree," then you are considered unmarried for tax purposes. In that case you should file as single (or head of household if you qualify) and you would not need your husband's SSN. When TurboTax asks your marital status you can select "legally separated."
If you have been separated "for many years," how have you filed your tax return in previous years?
